We study the Sturm-Liouville boundary value problem associated with the planar differential system $Jz'=\nabla V(z) + R(t, z)$, where $V(z)$ is positive and positively $2$-homogeneous and $R(t, z)$ is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed.
Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane
BOSCAGGIN, Alberto;GARRIONE, Maurizio
2016-01-01
Abstract
We study the Sturm-Liouville boundary value problem associated with the planar differential system $Jz'=\nabla V(z) + R(t, z)$, where $V(z)$ is positive and positively $2$-homogeneous and $R(t, z)$ is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed.
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